Finite Group Databasebeta

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C₂×C₉×D₁₉×C₄₃ #44440901

order	29412
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₄₃ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×D₁₉×C₄₃

Splittings

Fitting	C₂×C₉×C₁₉×C₄₃ ⋊ C₂
derived, Sylow	C₁₉ ⋊ C₂²×C₉×C₄₃
Hall	C₉×C₁₉×C₄₃ ⋊ C₂²
Hall	C₁₉×C₄₃ ⋊ C₂²×C₉
Hall	C₉×C₁₉ ⋊ C₂²×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₄₃	D₁₉
commutator, hypocenter	C₁₉	C₂²×C₉×C₄₃
Frattini	C₃	C₂×C₃×D₁₉×C₄₃
Fitting	C₂×C₉×C₁₉×C₄₃	C₂
socle	C₂×C₃×C₁₉×C₄₃	C₂×C₃
prime radical	C₂×C₃×D₁₉×C₄₃	C₃
cosocle	C₃×C₁₉	C₂²×C₃×C₄₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₉×C₄₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 14706

Conjugacy classes & character table

8514 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29412, 63);